Sure some thin ringed osage bows can survive successfully unbacked. However your end grain shows a hell of lot of earlywood, ie weak rings. Good thin ringed stuff looks predominantly dark on the end grain.
Rawhide back at the least. You would be better off planing the back down and gluing on some hickory.etc
I have seen unbacked osage with thin rings not survive first brace, and others that pop splinters on the back well after finishing tillering, when you would normally deem it to be a safe and successful bow.
Then again some people make bows that work through shear dumb luck, despite having thin rings, uncompensated for knots, and drawknife cuts digging into the back. Most people will have better results stacking the odds in their favour with a backing.